Is it proper to wear shorts in Monte Carlo and Monaco ? What about Venice, Dubrovnik and Kotor ?
The general rule is the more resorty the location, and the warmer the weather, the more likely you will see people in shorts.
If you intend to go into the Casino in Monte Carlo, check the dress restrictions.
This will general a lot of silly discussion ranging from wear from what you want to no. In general, Europeans, especially men, are not as quick to wear shorts as they are in the US. In many locations churches will require shoulders and knees covered for entry. On the walk along the beach or on the beach at Nice shorts are fine as is top less. I personally would not wear shorts but you can make your own decision.
Have been with my family, husband and 2 sons, to all of your above-mentioned destinations except Kotor and we wore shorts to all. The entire family. Not short shorts but knee length. We had no intentions of going into the casino in Monte Carlo so weren't worried about being underdressed. It was during the months of either June or July and it was hot.